Model Description
In this case, the surface water level is modeled by a first order differential equation. There are six sections with equal area that are allocated water based on institutions that determine how long each sector receives water, and in what order. Water is allocated to a given sector by opening and closing gates along the irrigation canals. Based on these allocations, each sector maintains a crop yield depending on the amount of time that maintains their water level within the bounds of a desired water height. When a sector receives less water than is desirable, yields decrease depending on the cumulative water stress (area on the curve between actual and desired water height). Water needs for each sector depends on the stage.
Default Dynamics
(Please describe default dynamics for this model.)
$dy/dt = \frac{u_n - \phi_n y_n}{A_n}$ |
| n represents the sector number, U represents the combination of check gates. For instance, U1=uB−u1. A represent the area of the section. A1, A2, A3, A4, A5, and A6 represents each sectors. ϕ represents the evapotranspiration/leakage/seepage which is considered same for all sections. The six sectors are linked by the check gates and canals which acts as nodes in the flow network. The flow of water and the timing of water flow are controlled by these gates. The depth equations based on physical configuration for each individual sectors are linked with the equation. The last equation regarding U are the combination of check points for each sectors that accounts the rules for water entering and leaving each node) This is the equation used to model the surface water level by first order differential order. There are six sectors and the model will be used for each sector respective to the area, the combination of check gates. |
par A1=11.67, A2=11.67, A2=11.67, A3=11.67, A4=11.67, A5=11.67 par A6=11.67 #yn is the standing water height #un is the combination of check gates #AN is the area of the sector #theta is evapotranspiration/leakage/seepage #Ua..D is water flow rates through the check points dy1/dt=(ub-u1-theta*y1)/A1 dy2/dt=(uc-u2-theta*y2)/A2 dy3/dt=(u2-u3-theta*y3)/A3 dy4/dt=(ua-u4-theta*y4)/A4 dy5/dt=(ud-u5-theta*y5)/A5 dy6/dt=(u4-u6-theta*y6)/A6
. 2010. Robustness, vulnerability, and adaptive capacity in small-scale social- ecological systems: The Pumpa Irrigation System in Nepal. Ecology and Society. 15(2):39-70.
